What is Universal gravitation: Definition and 148 Discussions
Newton's law of universal gravitation is usually stated as that every particle attracts every other particle in the universe with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. The publication of the theory has become known as the "first great unification", as it marked the unification of the previously described phenomena of gravity on Earth with known astronomical behaviors.This is a general physical law derived from empirical observations by what Isaac Newton called inductive reasoning. It is a part of classical mechanics and was formulated in Newton's work Philosophiæ Naturalis Principia Mathematica ("the Principia"), first published on 5 July 1687. When Newton presented Book 1 of the unpublished text in April 1686 to the Royal Society, Robert Hooke made a claim that Newton had obtained the inverse square law from him.
In today's language, the law states that every point mass attracts every other point mass by a force acting along the line intersecting the two points. The force is proportional to the product of the two masses, and inversely proportional to the square of the distance between them.The equation for universal gravitation thus takes the form:
F
=
G
m
1
m
2
r
2
,
{\displaystyle F=G{\frac {m_{1}m_{2}}{r^{2}}},}
where F is the gravitational force acting between two objects, m1 and m2 are the masses of the objects, r is the distance between the centers of their masses, and G is the gravitational constant.
The first test of Newton's theory of gravitation between masses in the laboratory was the Cavendish experiment conducted by the British scientist Henry Cavendish in 1798. It took place 111 years after the publication of Newton's Principia and approximately 71 years after his death.
Newton's law of gravitation resembles Coulomb's law of electrical forces, which is used to calculate the magnitude of the electrical force arising between two charged bodies. Both are inverse-square laws, where force is inversely proportional to the square of the distance between the bodies. Coulomb's law has the product of two charges in place of the product of the masses, and the Coulomb constant in place of the gravitational constant.
Newton's law has since been superseded by Albert Einstein's theory of general relativity, but it continues to be used as an excellent approximation of the effects of gravity in most applications. Relativity is required only when there is a need for extreme accuracy, or when dealing with very strong gravitational fields, such as those found near extremely massive and dense objects, or at small distances (such as Mercury's orbit around the Sun).
I need help with understanding this problem. I had initially chosen B, that the two satellites had the same speed because the mass does not effect the velocities of each of the satellites considering they are in orbit. But that answer was marked incorrect by my instructor. What other answer...
For question A, I know that I am supposed to input the numbers given into the Universal Gravitation Equation, but I do not know how to solve for it beyond that.
For question B, I know that the astronauts weight depends on the mass and gravity of the new planet but I do not know how to prove it...
Hello, and thank you again to anyone who can confirm if I have the right answer or who can give me some suggestions. This question felt like a bit of a surprise because we have not yet covered one where the mass of a planet was missing. Thus, my confidence in my work is low. Part b felt like a...
I tried to solve for mass of the mountain by:
(mass of ball) (9.8m/s^2)= G(mass of ball)(mass of mountain)/ (15000m)^2
The mass of the ball cancels out leaving with mass of mountain=33.04 * 10^(18) kg.
I didn't use Kepler's 3rd law and this may be the reason I have a wrong answer.
However, I want to know: where I make the mistake.
## ma = \frac {G M m} {R^2}##
## R = (\frac {G M} a)^{1/2}##
##a = \frac {v^2} R##
##V^2 = a R = a (\frac {G M} a)^{1/2} = (G a M)^{1/2}##
##V = (G a M)^{1/4}##...
Is gravitational prospecting pseudoscience?
From the literature, it says that we can know what is beneath a site (say for prospecting for oil. metals, etc) from measuring the local "g" field/acceleration at various locations. Together with other information, we can know the mass distributions...
Homework Statement
You are on a deep space mission to search for Earth-like planets. Your crew locates a possible planet and with scanners finds the radius to be 7.5 x 106 m. A team lands on the surface. There, they hang a 1.0 kg mass from a spring scale. It reads 8.5 N. Determine the mass of...
Homework Statement
earth has a mass of 5.98x10^24 kg and the moon has a mass of 7.35x10^22 kg. The distance from the centre of the moon to the centre of the Earth is 3.84x10^8 m. A rocket with a total mass of 1200 kg is 3.0x10^8 m from the centre of the Earth and directly in between Earth and...
Homework Statement
4 10kg objects are located at the corners of a rectangle sides 2 meters and 1 meter. Calculate the magnitude of gravitational force on 1 due to the other 3.
(Same sort of idea)
3 1kg objects are located at the corners of an equilateral triangle of side length 1 meter...
Homework Statement
ANY HELP IS WELCOMED[/B]
The single moon of an Earth-like planet creates tides on the planet that are slowing the planet’s rotation. The planet’s rate of rotation is decreasing at a rate of 7.00 x 10-7 radians/sec/century. The mass of the planet is 6 x 1024 kg, and its...
Homework Statement
The single moon of an Earth-like planet creates tides on the planet that are slowing the planet’s rotation. The planet’s rate of rotation is decreasing at a rate of 7.00 x 10-7 radians/sec/century. The mass of the planet is 6 x 1024 kg, and its diameter is 12,600 km. The...
Homework Statement
[/B]
Two 100-kg thrill seekers are diving into a neutron star. The neutron star’s mass is 1.1 solar masses and its radius is 12.0 km. For safety, they tie themselves together with a cord 10m long, so that as Melvin reaches the surface of the neutron star, Fred is 10.0 m...
Homework Statement
Show that the rate of change of the free-fall acceleration with vertical position near the Earth's surface is
\frac{d}{dr} [g] = -\frac{2GM_E}{R_E^3}
Assuming h is small in comparison to the radius of the Earth, show that the difference in free-fall acceleration between...
Homework Statement
http://[url=http://postimg.org/image/f7e6kp0xv/][PLAIN]http://s21.postimg.org/f7e6kp0xv/image.jpg
Homework Equations
Kepler's laws
The Attempt at a Solution
I thought the answer will be C : I and II
But the solution written (it was my friends book) is B, which is correct?
Homework Statement
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Given,
Mass of the Earth = 6*1024
Mass of Satellite = 45 kg
Radius of Satellite's orbit = 4.2*107
G = 6.67*10-11
Find the velocity of the satellite.
Homework Equations
Gravitational Force Fg = (G*Me*Ms)/(Rs2)
Newton's second law:
Fg = Ms*a where a...
I am writing a paragraph on astrophysicists. I want to incorporate a connection between the physics that we are learning and an astrophysicist's use of the same principles in their studies. Unfortunately, there is not much information about this on the internet.
What I have found is that...
Homework Statement
A piece of an empty rocket booster fuel tank (mass 45 kg) is ejected from a rocket that is 2100 km above the Earth's surface. It is traveling upwards at 4.5km/s at this time.
a) what is the total energy of the booster at this time?
b) Will it return to earth?
Homework...
Homework Statement
PART 1: Objects with masses of 125 kg and 548 kg are separated by 0.385 m. A 63.5 kg mass is placed midway between them.
Find the magnitude of the net gravitational force exerted by the two larger masses on the 63.5 kg mass. The value of the universal gravitational constant...
Homework Statement
I am currently reading about Newton's Law of Universal Gravitation and I am so confused as to why there is a negative sign in front of the equation Fg = (G* m1m2)/r^2.
Homework Equations
Fg = (G* m1m2)/r^2
There is a vector form of the magnitude of the gravitational force...
Homework Statement
Three point particles are fixed in place in the xy plane. The three partiles sit on the
corners of an equilateral triangle with sides of length a = 2.50 mm. Particle 1 has a mass m1 = 12.0 kg,
particle 2 has a mass m2 = 18.0 kg, and particle 3 has a mass m3 = 15.0 kg.
1...
Homework Statement
What is the gravitational force between Earth and the sun if the Earth has a mass of 5.98 x 10^24 and the sun has a mass of 1.99 x 10^30. The r is (1.5 x 10^11)^2[/B]Homework Equations
F=(Gm1m2)/r^2
G= 6.67 x 10^-11 N m^2 /kg^2 ( note that this is a constant)[/B]The...
If a bullet is fired vertically from the surface of the Earth with initial velocity v = 10 km / s, ignoring air resistance, at which distance h from the center of the Earth would arrive? (The radius of the Earth is RT = 6360 km, and the mass of the Earth MT = 5.98x10^24 kg)
I used the formula...
Homework Statement
On Earth, an average person's vertical jump is 0.40m. What is it on the Moon?
Homework Equations
Fg 1 on 2 = G(m1m2/r^2)
G= 6.67 x 10^-11
The Attempt at a Solution
r= 0.40m
F Earth on person on Earth's surface = 6.67x10^-11(m Earth x m person)/(0.40)^2
r=?
G moon = ?
F moon...
Homework Statement
The acceleration of gravity on the Moon is 1/6 what it is on Earth. The radius of the Moon is 1/4 that of the Earth. What is the Moon's mass compared to the Earth's?
Homework Equations
F_g = \frac{GMm} {r^2}
=> mg = \frac{GMm} {r^2}
=> g = \frac{GM} {r^2}
=> M = \frac{gr^2}...
If f dimensions are ml/t^2, where does t^2 come from in the equation of
F = G*m1*m2/r^2 where I believe G to be a constant, m1 and m2 to be masses and r to be the distance between two masses - so length. To dimensionally analyse this then, where would the dimension time come from if I were to...
Hi all, I'm currently a student teacher. Next week I'm going to teach a lesson on universal gravitation to grade 11 students. It's the first lesson on the topic, so it will be an introduction and not too in-depth.
I'm struggling with ways to make it interesting. I decided to start the lesson...
Homework Statement
its 3.8 x 10^8 from Earth's core to the lunar's core
calculate the gravitational attraction exerted by Earth on the moon
Homework Equations
ag = GM/ r^2
G= 6.67 x 10^-11
M of earth= 5.98 x 10^24 ... r= 6.37 x 10^6
M of moon= 7.36 x 10^22 ... r= 1.74 X...
Homework Statement
In the not-too-distant future astronauts will travel to Mars to carry out scientific explorations. As part of their mission, it is likely that a "geosynchronous" satelite will be placed
above a given point on the Martian equator to facilitate communcations. At what altitude...
Homework Statement
Particle A having mass mA is placed at a fixed distance r from particle B which has twice the mass of particle A. Which of the following statements will be true?
Select one:
a. The magnitude of the force on A will be twice the magnitude of the force on B.
b. The...
Homework Statement
Having problems on the method of calculating the acceleration due to gravity of the planet.
A certain planet has a diameter of 1715 km and a density of 5254 kg/m³. The planet has a moon that orbits every 4.46 earth-days.
What is the acceleration due to gravity...
Hello, physicsforums. I'm trying to write a proof for a function involving Newton's law of gravitation, and I seem to be stuck. The function I'm trying to build is a function of time with respect to distance.
This is the formula I want to transform.
\mathrm{A}=-\frac{GM}{x^{2}}
For...
Homework Statement
The radius of the Earth is 6400km. A 7200n spacecraft travels away from the earth. what would be the weight of the spacecraft at the following distances from the Earths surface: 6400km, 12800km
Homework Equations
Fg=mg
F=Gm1m2/r^2
The Attempt at a Solution
Just...
Homework Statement
This question is from the Nelson Grade 12 Physics textbook.
The force of attraction between masses m1 and m2 is 26N in magnitude. What will the magnitude of the force become if m2
is tripled, and the distance between m2 and m1 is halved?
Homework Equations...
Universal Gravitation Constant - HELP!
Hello, I'm a little confused...
What is the difference between the "Constant of Universal Gravitation" and the "Gravitational Force"? I know that there is a radius between two or more objects like the Earth and the Moon and bla bla bla... But the thing...
Homework Statement
A star of mass 5 × 10e30 kg is located at ‹ 7 × 10e12, 3 × 10e12, 0 › m. A planet of mass 4 × 10e24 kg is located at ‹ 5 × 10e12, 5 × 10e12, 0 › m and is moving with a velocity of ‹ 0.6 × 10e4, 1.4 × 10e4, 0 › m/s.
A. During a time interval of 1x10e6 seconds, what is the...
##F = G \frac{ m_{1} m_{2}}{ r^{2} } ##
Where does the formula come from? And why does it work that way?
How would it relate to Newton's Second Law?
##F = ma##
Using Newton's Second Law, is it possible to get the Law of Universal Gravitation?
Homework Statement
The electric field, E, a distance D away from a charged particle is directly proportional to the size of the charge Q, and inversely proportional to the square of the distance D. If the charge is increased by 40% and the distance is increased by 30%, by what percentage does...
Hi guys,
I'm not sure if I'm going about this the correct way, but it seems to be the only one that makes sense right now. The problem reads: Io, a satellite of Jupiter, has an orbital period of 1.77 days and an orbital radius of 4.22E5 km. From these data, determine the mass of Jupiter...
Homework Statement
What is the distance from the Earth's center to a point outside the Earth where the gravitational acceleration due to the Earth is 1/10 its value at the Earth's surface?Homework Equations
FG= GmM/r^2
g= Gm/r^2
G=6.67x10^-11 (Nm^2)/kg^2
m(earth)=5.97x10^24 kg
g=9.8m/s^2
The...
Homework Statement
The force of gravity on a spacecraft some distance from Earth is 900 N. What will be the force of gravity on a spacecraft with twice the mass, at a distance from Earth’s centre that is as far?
Homework Statement
A student proposes to study the gravitational force by suspending 2 100 kg sperical objects at the lower ends of cables from the ceiling of a tall cathedral and measuring the deflection of the cables from the vertical. The 45 m long cables are attatched to the ceiling 1m...
Homework Statement
A planet's mean distance from the sun is 2.00x10^11 m. Determine the planet's orbital period. Use information found in textbook.
Homework Equations
So I use the following equations:
R=h+Rs
T=2∏√(R3/GxMs)
From the textbook I got the following values...
Homework Statement
As the Earth revolves around the sun, if not only travels a certain distance every second, it also causes an imaginary line between the Earth and the sun to pass through a certain area every second. During one complete trip around the sun, the total area would be...
Homework Statement
Two bags of apples, each containing 20 apples of equal mass, experience a gravitational force of attraction of 200 units when separated by a distance of 25.0cm. If 10apples are removed from one bag and placed into the other bag, and the two bags are separated by the same...
Homework Statement
One of the moons of Jupiter, discovered by Galileo, has an orbital period of 1.44x106s and a mean orbital radius from the centre of Jupiter of about 1.90x109m. From this information, determine the mass of planet Jupiter.
Homework Equations
I have made a list of...
Homework Statement
Determine the speed of a satellite moving in a stable orbit about the Earth if the satellite is 525 km above the Earth's surface.
Homework Equations
I have made a list of equations that are relevant for this entire module on universal gravitation. So although there are...
Homework Statement
Michael has a mass of 75.0 kg and Elaine has a mass of 55.0 kg. If Michael and Elaine are 2.50 m apart from each other as they sit in their Physics class, determine the gravitational force of attraction between them.
Homework Equations
I have made a list of equations...